Continuity of solutions to the G-Laplace equation involving measures
We establish local continuity of solutions to the G-Laplace equation involving measures, i.e., −div � g(|∇u|) |∇u| ∇u where µ is a nonnegative Radon measure satisfying µ(Br(x0)) ≤ Crm for any ball Br(x0) ⊂⊂ Ω with r ≤ 1 and m > n − 1 − δ ≥ 0. The function g is supposed to be nonnegative and C 1 -...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Elliptikus differenciáloperátor, Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.39 |
| Online Access: | http://acta.bibl.u-szeged.hu/62117 |
| Tartalmi kivonat: | We establish local continuity of solutions to the G-Laplace equation involving measures, i.e., −div � g(|∇u|) |∇u| ∇u where µ is a nonnegative Radon measure satisfying µ(Br(x0)) ≤ Crm for any ball Br(x0) ⊂⊂ Ω with r ≤ 1 and m > n − 1 − δ ≥ 0. The function g is supposed to be nonnegative and C 1 -continuous on [0, +∞), satisfying g(0) = 0 and tg0 (t) g(t) ≤ g0, ∀t > 0 with positive constants δ and g0, which generalizes the structural conditions of Ladyzhenskaya–Ural’tseva for an elliptic operator. |
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| Terjedelem/Fizikai jellemzők: | 1-10 |
| ISSN: | 1417-3875 |